The Nano second that legal law were brought up means all bets are off. When someone threatens legal action for rights to you child, they have said I will sue you for custody/partial custody of your child.

If they can prove any relationship, they may get a toehold. Now whether they win or not, they can still drag you through the legal mud and ruin you financially.

You need a lawyer, experienced and certified in your jurisdiction, on how to proceed. NY treats GPR as a god given right, FL laughs at them.

Whatever you do, do not try and appease the beast, by offering a peace offering meeting. Save every text and email and FB message, print them out, keep digital copies.